Stability estimates for the identification of nonlinear heat transfer laws
- 1 October 1996
- journal article
- Published by IOP Publishing in Inverse Problems
- Vol. 12 (5), 743-756
- https://doi.org/10.1088/0266-5611/12/5/015
Abstract
Consider the heat equation with a nonlinear function in the boundary condition which depends only on the solution u of the initial-boundary-value problem. The unknown function belongs to a set of admissible uniformly Lipschitz continuous functions. For this problem stability estimates of the form with different norms are derived. Finally an interesting example is discussed.Keywords
This publication has 6 references indexed in Scilit:
- Fréchet Differentiability of the Solution of the Heat Equation with Respect to a Nonlinear Boundary ConditionZeitschrift für Analysis und ihre Anwendungen, 1996
- Error estimates for regularized solutions of non-linear ill-posed problemsInverse Problems, 1994
- Identification of nonlinear heat transfer laws by optimal controlNumerical Functional Analysis and Optimization, 1994
- Estimation of a temporally and spatially varying diffusion coefficient in a parabolic system by an augmented Lagrangian techniqueNumerische Mathematik, 1991
- The Augmented Lagrangian Method for Parameter Estimation in Elliptic SystemsSIAM Journal on Control and Optimization, 1990
- Identification de la Non-Linearité D'Une équation Parabolique QuasilineaireApplied Mathematics & Optimization, 1974